docs: def getFreeEnergyDifferences(self, compute_uncertainty=True, uncertainty_method=None, warning_cutoff=1.0e-10, return_theta=False):
          """Get the dimensionless free energy differences and uncertainties among all thermodynamic states.
  
  
          Parameters
          ----------
          compute_uncertainty : bool, optional
              If False, the uncertainties will not be computed (default: True)
          uncertainty_method : string, optional
              Choice of method used to compute asymptotic covariance method,
              or None to use default.  See help for computeAsymptoticCovarianceMatrix()
              for more information on various methods. (default: svd)
          warning_cutoff : float, optional
              Warn if squared-uncertainty is negative and larger in magnitude
              than this number (default: 1.0e-10)
          return_theta : bool, optional
              Whether or not to return the theta matrix.  Can be useful for complicated differences.
  
          Returns
          -------
          Deltaf_ij :L np.ndarray, float, shape=(K, K)
              Deltaf_ij[i,j] is the estimated free energy difference
          dDeltaf_ij :L np.ndarray, float, shape=(K, K)
              dDeltaf_ij[i,j] is the estimated statistical uncertainty 
              (one standard deviation) in Deltaf_ij[i,j]
  
          Notes
          -----
          Computation of the covariance matrix may take some time for large K.
  
          The reported statistical uncertainty should, in the asymptotic limit, reflect one standard deviation for the normal distribution of the estimate.
          The true free energy difference should fall within the interval [-df, +df] centered on the estimate 68% of the time, and within
          the interval [-2 df, +2 df] centered on the estimate 95% of the time.
          This will break down in cases where the number of samples is not large enough to reach the asymptotic normal limit.
  
          See Section III of Reference [1].
  
          Examples
          --------
  
          >>> from pymbar import testsystems
          >>> (x_n, u_kn, N_k, s_n) = testsystems.HarmonicOscillatorsTestCase().sample(mode='u_kn')
          >>> mbar = MBAR(u_kn, N_k)
          >>> [Deltaf_ij, dDeltaf_ij] = mbar.getFreeEnergyDifferences()
  
          """
  
          # Compute free energy differences.
          f_i = np.matrix(self.f_k)
          Deltaf_ij = f_i - f_i.transpose()
  
          # zero out numerical error for thermodynamically identical states
          self._zerosamestates(Deltaf_ij)
  
          returns = []
          returns.append(np.array(Deltaf_ij))
  
          if compute_uncertainty or return_theta:
              # Compute asymptotic covariance matrix.
              Theta_ij = self._computeAsymptoticCovarianceMatrix(
                  np.exp(self.Log_W_nk), self.N_k, method=uncertainty_method)
  
          if compute_uncertainty:
              # compute the covariance component without doing the double loop.
              # d2DeltaF = Theta_ij[i,i] + Theta_ij[j,j] - 2.0 * Theta_ij[i,j]
  
              diag = Theta_ij.diagonal()
              d2DeltaF = diag + diag.transpose() - 2 * Theta_ij
  
              # zero out numerical error for thermodynamically identical states
              self._zerosamestates(d2DeltaF)
  
              # check for any numbers below zero.
              if (np.any(d2DeltaF < 0.0)):
                  if(np.any(d2DeltaF) < warning_cutoff):
                      # Hmm.  Will this print correctly?
                      print("A squared uncertainty is negative.  d2DeltaF = %e" % d2DeltaF[(np.any(d2DeltaF) < warning_cutoff)])
                  else:
                      d2DeltaF[(np.any(d2DeltaF) < warning_cutoff)] = 0.0
  
              # take the square root of the entries of the matrix
              dDeltaf_ij = np.sqrt(d2DeltaF)
  
              # Return matrix of free energy differences and uncertainties.
              returns.append(np.array(dDeltaf_ij))
  
          if (return_theta):
              returns.append(np.array(Theta_ij))
  
          return returns